1. VIII Measure - Capability and Measurement

2. Initial Thoughts
Success depends upon the ability to measure performance. Rule #1: A process is only as good as the ability to reliably measure. Rule #2: A process is only as good as the ability to repeat. Gordy Skattum, CQE
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3. Initial Thoughts
It is impossible for us to improve our processes if our gaging system cannot discriminate between parts or if we cannot repeat our measurement values.
Every day we ask “Show me the data” - yet we rarely ask is the data accurate and how do you know?
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4. Purpose of Measurement
Product Control
Detection, conformance to a design specification
Process Control
Prevention, real-time control, assessing a feature to its natural process variation
What is a measurement system used for?
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5. AIAG/MSA/Gage R&R AIAG – Automotive Industry Action Group
Collaboration between “Big 3” to create one set of guidelines for all suppliers
MSA Reference Manual – Measurement System Analysis
Introduction to MSA
Covers normally occurring measurement situations
Developed to meet specific needs of the automotive industry
Gage Repeatability and Reproducibility
A study to understand the within-system and between-system variation in a measurement system
A comparison of standard deviation
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6. Measurement Terms Discrimination
In selecting or analyzing a measurement system, we are concerned about the system’s discrimination, or the capability of the system to detect and faithfully indicate even small changes of the measured characteristic - also known as resolution.
The smallest readable unit
100ths graduation decimal rule
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7. Accuracy vs. Precision Precise (low variation) Yes No No
Accurate (on target)
Yes
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8. MSA Terms Bias Choices for addressing bias error
The difference between the observed average of measurements and the reference value. The reference value, also known as the accepted reference value or master value, is a value that serves as an agreed-upon reference for the measured values. Bias is measured as “accuracy” or as “accuracy shift.”
Choices for addressing bias error
Calibrate the gage; adjust, correct, or apply an offset
Change the system (instrument, condition, masters, …)
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9. MSA Terms Stability Time 2 Time 1
Stability (or drift) is the total variation in the measurements obtained with a measurement system on the same master or parts when measuring a single characteristic over an extended time period.
The change in bias over time.
Stability
Time 2
Time 1
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10. MSA Terms Linearity Choices for addressing linearity
Linearity is the bias over the operating range of a measurement system. This, along with bias, is checked as part of the calibration procedure.
Choices for addressing linearity
Calibrate, adjust the gage or build offset table
Change the system (condition, masters, …)
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11. MSA Terms Repeatability (EV)
Repeatability is the variation in measurements obtained with one measurement instrument when used several times by one appraiser while measuring the identical characteristics on the same part. Includes all within-system variation.
Repeatability
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12. MSA Terms Reproducibility (AV)
Reproducibility is the variation in the average of the measurements made by different appraisers using the same measuring instrument when measuring the identical characteristics on the same part. Includes all between-system variation.
Operator A
Operator B
Operator C
Repeatability
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13. Effective Resolution
The sensitivity of a measurement system to detect process variation
Rules for determining effective resolution
Count the number of “0” plot points on the process range control chart. If >25%, then the gage lacks effective resolution
Count the gage discrimination levels between the UCL and the LCL of the process average control chart. If <5 levels, gage lacks effective resolution
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14. Effective Resolution Levels between UCL-LCL? Number of zeros?
Individuals Chart
UCL=5.2633
LCL=
CEN=2.16 -2 2 4 6 1 3 5 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Moving R Chart
UCL=3.8115
LCL=0.0
CEN=1.1667 -1
Levels between UCL-LCL?
Number of zeros?
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15. Gage R&R Levels A capability measure Typically we compare
Gage R&R to tolerance
Gage R&R to process variation
Three levels of results
0-10% 
10-30% 
+30% 
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16. Impact on SPC and 6s If you have a poor measurement system…
Difficult/impossible to make process improvements
Causes quality / cost / delivery / responsiveness problems
False alarm signals, increases process variation, loss of process stability
Improperly calculated control limits
Can make your processes worse!
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17. Guidelines for Determining a Gage R&R
Since the purpose of the analysis of a measurement system is to understand the systems variation, the use of graphical tools is very important. Personal investigations have unveiled many powerful gage analysis software packages.
SPCXL (Sigma Zone)
Minitab
All will deliver identical results*
SPCXL is easy to use and inexpensive.
Minitab is a complete statistical analysis package which requires a lot of training.
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18. Guidelines (cont.)
The four standard methods for analyzing measurement systems are:
Range method (short form)
Average and Range (long form)
ANOVA (Analysis of Variance)
Attribute gage study (both short and long form methods)
Each method has its advantages and disadvantages as well as limitations.
Refer to the AIAG MSA Reference Manual (Measurement Systems Analysis) for additional information.
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19. Initial Control Chart Analysis
Our first concerns are about the measurements systems discrimination (meet 10:1 rule?)
We can determine if the measurement system has adequate discrimination by reviewing the process control charts for the process ahead of time. (effective resolution? stable?)
We need to make sure we study parts over the total range for the process or tolerance, whichever is greater
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20. Preparation for Conducting a GR&R Study
The approach to be used should be well planned out.
Determine the number of appraisers, sample parts, and trials in advance.
The appraisers chosen should be selected from those who normally operate the instrument.
The sample parts selected must represent at least the entire range of the process.
Each part will be marked for identification.
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21. Preparation (cont.) Verify use of the 10:1 rule.
Assure that the appraisers method of measuring the characteristics feature is following the defined measurement procedure. Each should use the same technique.*
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22. Preparation (cont.)
To minimize the likelihood of misleading results, the following steps should be taken:
The measurements should be made in a random order. The appraisers should be unaware of which numbered part is being checked in order to avoid any possible knowledge bias.
In reading the equipment, the readings should be estimated to the nearest resolution that can be obtained. If possible, readings should be made to one-half of the smallest resolution.
YOU must oversee the entire study so that bias’ does not occur.
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23. Gage R&R Sheet Available on Website
Quality Tools.xlsx
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24. Analysis of Results
Following are examples of gage analysis charts one would find using SPCXL.
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25. Results (cont)
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26. Total Variance
The total amount of variance in the gage and in the process
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27. What Happens When “Shift Happens”?
Most processes are designed to meet the customer specification
Because we are using all of our tolerance, we’re forced to keep the process exactly centered.
If the process shifts at all, nonconforming parts will be produced
Target
Lower Limit
Upper Limit
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28. Getting Started
Using 75% or less of a tolerance will allow processes to shift slightly without producing any defects.
The goal is to improve your process in order to use the least amount of tolerance possible
Reduce the opportunity to produce defects
Reduce the cost of the process
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29. Potential Process Capability Index (Cp)
Defines the width of the process distribution
Cp is calculated by dividing the tolerance zone width by the width of the +/- 3 sigma distribution
This Cp number (or index) tells how many times the distribution will fit into the tolerance zone
A Cp of at least 1.33 is desired *
* Which standard deviation do I use?
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30. What it Looks Like…
If a process uses 50% of a tolerance zone, the Cp value would be 2.0
If a process uses 100% of the tolerance zone, the Cp value would be 1.0
If a process uses 200% of the tolerance zone, the Cp value would be 0.5
The higher the number, the more precise the process distribution and the more potentially capable the process is of meeting the specification.
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31. Capability Ratio (CR) Process capability as a percentage of tolerance
The inverse of the calculations for Cp
Divide the width of the +/- 3 sigma distribution by the width of the tolerance zone
A CR of no more than .75 is desired *
* Which standard deviation do I use?
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32. Calculating CR If a processes Cp = 1.0 the CR = 100%
neat
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33. Actual Process Capability (Cpk)
Takes into account not only the spread of the distribution, but also the location of it as well
A Cpk of at least 1.33 is desired
Calculating Cpk: * *
* Which standard deviation do I use?
Cpk = Cp - a “Penalty” for off-center distributions!
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34. What it Looks Like...
If a process uses 100% of a tolerance zone, Cp = 1.0
If the distribution is not centered, the Cpk <1.0
Cpk = Cpk <1.0
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35. What it Looks Like (cont.)
If a process uses 1/2 of the tolerance zone, the Cpk = 2.0
If the process is not centered, the Cpk value would be <2.0
Cpk = Cpk <2.0
LSL USL
Target
LSL USL
this stuff is
so awesome
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36. PROCESS CAPABILITY “Cp”, “CR” & “Cpk”
Low
Speed Limit
High
Speed Limit
MEAN 1s 65 70 75 *
Cp =
USL - LSL 6s *
Cpk =
MEAN - LSL 3s *
6 s
Min
CR =
USL - LSL
Cpk =
USL - MEAN 3s
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37. Where Do I Improve? Control then capability 1st Shape – control chart
Stabilize process
Am I in control?
2nd Spread – Cp
Reduce variation
Cp>1.33?
3rd Location – Cpk
Center process
Cpk>1.33?
Control then capability
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38. What Cp and Cpk Can Tell Us
We can determine next steps to improve the process by comparing the Cp and Cpk numbers. For example:
High Cp, high Cpk…
Process is centered (accurate) and capable (precise). No improvements are needed.
High Cp, low Cpk…
Process is capable (precise) but not centered (accurate).
Improvements should shift the process mean to match the target.
Low Cp, low Cpk…
Process is not centered (accurate), and variation must be reduced to be precise.
<Write some Cp and Cpk numbers on a flip chart or on a white board to illustrate these three concepts> Remember, shifting the mean of a capable process to make a process more accurate is relatively cheap. Improving a process by identifying and removing variation is more expensive – it’s usually a Green Belt or Black Belt project.
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39. Capability Indices Exercise
USL = 1.505
LSL =
s =
CR =
Cp =
USL = .507
LSL = .506
s =
USL = 2800 PPH
LSL = PPH
Xbar = 2750 PPH
s = 12.5PPH
Cpk =
USL = 750 Mhz
LSL = 735 Mhz
Xbar = 740 Mhz
s = 1.333Mhz
USL = 1.503
Xbar = 1.501
USL = .251
LSL = .250
Xbar = .250
s =
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